{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Martingales Regression.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNXG+fcjtG9XNEFnoaIE1ol",
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Farmhouse121/Adventures-in-Financial-Data-Science/blob/main/Martingales_Regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 462
        },
        "id": "pJmHmdbdrrjF",
        "outputId": "ad969f00-e783-48b7-d04d-af3b5e1d040c"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as pl ; golden_ratio=(1e0+np.sqrt(5e0))/2e0 ; figure_size=(7*golden_ratio,7)\n",
        "\n",
        "npts=100\n",
        "np.random.seed(123456) # so the plot is reliable, and this is not a \"mined\" seed, as is clear from it's value\n",
        "df=pd.DataFrame({'x':np.random.normal(size=npts),'y':np.random.normal(size=npts)})\n",
        "\n",
        "for column in df:\n",
        "    df[column]=df[column].cumsum()\n",
        "\n",
        "figure,plot=pl.subplots(figsize=figure_size)\n",
        "plot=df.plot(ax=plot)\n",
        "plot.set_xlabel(\"Observation Number\",fontsize=12)\n",
        "plot.set_ylabel(\"Series Value\",fontsize=12)\n",
        "plot.set_title(\"Two Martingales\",fontsize=14);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 815.489x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 884
        },
        "id": "wrssCfcs_tBS",
        "outputId": "e649b0d7-2174-4181-ac0d-5486d8a0e007"
      },
      "source": [
        "from statsmodels.formula.api import ols\n",
        "from statsmodels.sandbox.regression.predstd import wls_prediction_std\n",
        "alpha=0.05 # set alpha_critical to 5%\n",
        "fit=ols(\"y ~ x\",df).fit() # do OLS regression\n",
        "df['yhat']=fit.fittedvalues # get the fit\n",
        "print(fit.summary()) # print the regression summary\n",
        "\n",
        "figure,plot=pl.subplots(figsize=figure_size)\n",
        "df.plot.scatter(\"x\",\"y\",ax=plot)\n",
        "x,y,yhat=tuple(map(lambda c:df[c].tolist(),list(df)))\n",
        "sig,crl,cru,=wls_prediction_std(fit,alpha=alpha) # get the confidence regions with given alpha\n",
        "x,y,yhat,crl,cru=tuple(zip(*list(sorted(zip(x,y,yhat,crl,cru),key=lambda a:a[0])))) # sort all values by x\n",
        "plot.plot(x,yhat,'r-',label='Regression Line')\n",
        "plot.fill_between(x,crl,cru,alpha=0.2,label='%.0f%% Confidence Region' % (1e2-1e2*alpha))\n",
        "plot.set_title(\"Regression between Two Martingales\",fontsize=14)\n",
        "plot.legend(loc=\"best\");"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.693\n",
            "Model:                            OLS   Adj. R-squared:                  0.690\n",
            "Method:                 Least Squares   F-statistic:                     221.7\n",
            "Date:                Tue, 16 Nov 2021   Prob (F-statistic):           6.63e-27\n",
            "Time:                        17:58:11   Log-Likelihood:                -216.64\n",
            "No. Observations:                 100   AIC:                             437.3\n",
            "Df Residuals:                      98   BIC:                             442.5\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Intercept      4.3311      0.530      8.167      0.000       3.279       5.383\n",
            "x             -0.6435      0.043    -14.889      0.000      -0.729      -0.558\n",
            "==============================================================================\n",
            "Omnibus:                        2.039   Durbin-Watson:                   0.354\n",
            "Prob(Omnibus):                  0.361   Jarque-Bera (JB):                1.946\n",
            "Skew:                          -0.258   Prob(JB):                        0.378\n",
            "Kurtosis:                       2.551   Cond. No.                         30.7\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 815.489x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 464
        },
        "id": "NRU5kCtTAPvw",
        "outputId": "efc7b68d-9d52-4399-8851-aabe6b0b4031"
      },
      "source": [
        "f_stats=pd.DataFrame({'F':[],'p':[]})\n",
        "\n",
        "for i in range(1000):\n",
        "    df=pd.DataFrame({'x':np.random.normal(size=npts),'y':np.random.normal(size=npts)})\n",
        "\n",
        "    for column in df:\n",
        "        df[column]=df[column].cumsum()\n",
        "\n",
        "    fit=ols(\"y ~ x\",df).fit()\n",
        "    f_stats=f_stats.append(pd.DataFrame({'F':[fit.fvalue],'p':[fit.f_pvalue]}))\n",
        "\n",
        "print(\"Mean of F Statistics = %.2f [%.2f expected]\" % (f_stats[\"F\"].mean(),(npts-len(fit.params))/(npts-len(fit.params)-2)))\n",
        "\n",
        "figure,plot=pl.subplots(figsize=figure_size)\n",
        "f_stats['p'].plot.hist(ax=plot,bins=np.linspace(0,1,100))\n",
        "plot.set_title(\"Distribution of $p$ Value for Regressions of Two Martingales\",fontsize=14);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean of F Statistics = 55.68 [1.02 expected]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 815.489x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cxoa-YdDnayv",
        "outputId": "5862c3de-bf55-45b8-b905-b85f5d218e12"
      },
      "source": [
        "for column in df:\n",
        "     df[\"Δ\"+column]=df[column].diff()\n",
        "\n",
        "fit=ols('Δy ~ Δx',df).fit()\n",
        "print(fit.summary())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                     Δy   R-squared:                       0.027\n",
            "Model:                            OLS   Adj. R-squared:                  0.017\n",
            "Method:                 Least Squares   F-statistic:                     2.722\n",
            "Date:                Tue, 16 Nov 2021   Prob (F-statistic):              0.102\n",
            "Time:                        19:30:04   Log-Likelihood:                -123.98\n",
            "No. Observations:                  99   AIC:                             252.0\n",
            "Df Residuals:                      97   BIC:                             257.1\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Intercept      0.0662      0.086      0.770      0.443      -0.105       0.237\n",
            "Δx            -0.1282      0.078     -1.650      0.102      -0.283       0.026\n",
            "==============================================================================\n",
            "Omnibus:                        5.999   Durbin-Watson:                   2.131\n",
            "Prob(Omnibus):                  0.050   Jarque-Bera (JB):                2.721\n",
            "Skew:                           0.041   Prob(JB):                        0.257\n",
            "Kurtosis:                       2.192   Cond. No.                         1.12\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1xD_1HRYF3Hw"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}